Solve for $x$ and $y$ using elimination. ${-6x-2y = -32}$ ${-5x+3y = 20}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${-18x-6y = -96}$ $-10x+6y = 40$ Add the top and bottom equations together. $-28x = -56$ $\dfrac{-28x}{{-28}} = \dfrac{-56}{{-28}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-6x-2y = -32}\thinspace$ to find $y$ ${-6}{(2)}{ - 2y = -32}$ $-12-2y = -32$ $-12{+12} - 2y = -32{+12}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 2}$ into $\thinspace {-5x+3y = 20}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + 3y = 20}$ ${y = 10}$